系統識別號 | U0002-0207200517551100 |
---|---|
DOI | 10.6846/TKU.2005.00027 |
論文名稱(中文) | 含界層裂紋之彈壓電複合材料之動力破壞分析 |
論文名稱(英文) | Dynamic Fracture Analysis of an Interface Crack between Purely Elastic and Piezoelectric Materials. |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 航空太空工程學系碩士班 |
系所名稱(英文) | Department of Aerospace Engineering |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 93 |
學期 | 2 |
出版年 | 94 |
研究生(中文) | 蔡忠翰 |
研究生(英文) | Chung-Han Tsai |
學號 | 692370678 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | |
口試日期 | 2005-06-16 |
論文頁數 | 206頁 |
口試委員 |
指導教授
-
應宜雄
委員 - 馬劍清 委員 - 劉昭華 委員 - 應宜雄 |
關鍵字(中) |
複合壓電材料 界面裂紋 應力強度因子 動力破壞 |
關鍵字(英) |
piezoelectric interface crack stress intensity factor dynamic fracture |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
本文研究內含電極邊界彈壓電複合材料之界層裂紋的動力破壞問題,解析一含半無限長界面裂紋之彈壓電複合材料,於裂紋面上施予均佈反平面動力載荷之破壞行為,並研究於距離裂紋尖端h處之裂紋面分別為受一對反平面動力點載荷之暫態效應,本文使用積分轉換法與Wiener-Hopf技巧推導彈壓電複合材料於一次拉普拉氏轉換域中,受空間指數應力之基本解,並利用此基本解來解析此包含特徵長度的複合壓電材料動力暫態問題,接著使用Cagniard-de Hoop方法來作拉普拉斯逆轉換得到時域中的解。最後本文針對應力、電位移、應力強度因子與電位移強度因子等解析解,做詳細的數值計算與討論。 |
英文摘要 |
In this study, the transient response of a semi-infinite, interface crack between hexagonal piezoelectric and purly elastic media with the electrode boundary condition is investigated. The useful fundamental solutions are derived and the solutions can be determined by superposition of the fundamental solutions in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in Laplace transform domain) on the interface crack faces. The Cagniard-de Hoop method of Laplace inversion is used to obtain the transient solution in time domain. Exact transient Full-Field solutions to the problem with uniform loads, and exact transient solutions of intensity factors to the problem with concentrated loads are both derived. Finally, numerical results are evaluated and discussed in detail. |
第三語言摘要 | |
論文目次 |
目錄 目錄 ……………………………………………………………… I 圖表目錄 ………………………………………………………… V 第一章 緒論 ………………………………………………………1 1.1 研究動機 …………………………………………………1 1.2 文獻回顧 …………………………………………………3 1.3 內容簡介 …………………………………………………8 第二章 理論基礎與基本解 ………………………………………9 2.1 線彈性壓電材料之控制與本構方程式 …………………9 2.2 純彈性材料之控制與本構方程式 ……………………15 2.3 拉普拉斯轉換與Cagniard-de Hoop method …………16 2.3.1 拉普拉斯轉換 …………………………………………16 2.3.2 Cagniard-de Hoop method ……………………………17 第三章 半無窮長界面裂紋受反平面動力均佈載荷之全場解析 ……………………18 3.1 問題描述 ………………………………………………18 3.2 G(λ)函數拆解 …………………………………………24 3.3 N(λ)函數拆解 …………………………………………27 3.4 存在MT表面波之複合壓電材料之理論解析 …………38 3.4.1 壓電材料剪力波波速大於純彈性材料剪力波波速之拉普拉斯域解(bbg>b(e)) ………………………38 3.4.2 壓電材料剪力波波速大於純彈性材料剪力波波速之時域解(bbg>b(e)) ………………………………43 3.4.3 壓電材料剪力波波速小於純彈性材料剪力波波速之拉普拉斯域解 ……53 3.4.4 壓電材料剪力波波速小於純彈性材料剪力波波速之時域解 ……………56 3.5 V(λ)函數拆解 …………………………………………64 3.6 J(λ)函數拆解 …………………………………………67 3.7 無MT表面波之複合壓電材料之理論解析 ……………69 3.7.1 壓電材料剪力波波速大於純彈性材料剪力波波速之拉普拉斯域解(b(e)>bbg) ………………………69 3.7.2 壓電材料剪力波波速大於純彈性材料剪力波波速之時域解(b(e)>bbg) ………………………………73 3.7.3 壓電材料剪力波波速小於純彈性材料剪力波波速之拉普拉斯域解 ……80 3.7.4 壓電材料剪力波波速小於純彈性材料剪力波波速之時域解 ……………83 3.8 數值計算與討論 ………………………………………92 第四章 半無窮長界面裂紋受反平面動力點載荷之破壞解析 ………………………97 4.1 存在MT表面波之複合壓電材料之基本解 ……………97 4.1.1 壓電材料剪力波波速大於純彈性材料剪力波波速之基本解(bbg>b(e)) …………………………………97 4.1.2 壓電材料剪力波波速小於純彈性材料剪力波波速之基本解 ……………105 4.2 無MT表面波之複合壓電材料之基本解 ………………110 4.2.1 壓電材料剪力波波速大於純彈性材料剪力波波速之基本解(b(e)>bbg) ………………………………110 4.2.2 壓電材料剪力波波速小於純彈性材料剪力波波速之基本解 ……………115 4.3 問題描述 ………………………………………………120 4.4 存在MT表面波之複合壓電材料之理論解析 …………121 4.4.1 壓電材料剪力波波速大於純彈性材料剪力波波速之應力及電位移強度因子(bbg>b(e)) ……………122 4.4.2 壓電材料剪力波波速小於純彈性材料剪力波波速之應力及電位移強度因子 …………………………129 4.5 無MT表面波之複合壓電材料之理論解析 ……………131 4.5.1 壓電材料剪力波波速大於純彈性材料剪力波波速之應力及電位移強度因子(b(e)>bbg) ……………131 4.5.2 壓電材料剪力波波速小於純彈性材料剪力波波速之應力及電位移強度因子 …………………………133 4.6 數值計算與討論 ………………………………………135 第五章 成果與討論 ……………………………………………140 5.1 本文結論 ………………………………………………140 5.2 本文成果 ………………………………………………141 5.2 尚待研究的方向 ………………………………………142 參考文獻 …………………………………………………………144 圖表目錄 表3.1 PZT4搭配不同彈性材料之根的現象 ……………………162 表3.2 PZT4搭配不同彈性材料之波速比較表 …………………163 表3.3 壓電材料常數表 …………………………………………164 表3.4 純彈性材料常數表 ………………………………………165 圖3.1 界面裂紋之問題描述 ……………………………………166 圖3.2 S1之積分路徑圖 …………………………………………167 圖3.3a c(e)>c之λ平面圖 ………………………………………168 圖3.3b c>c(e)之λ平面圖 ………………………………………169 圖3.4a c(e)>c有根形式之v平面圖 ……………………………170 圖3.4b c(e)>c無根形式之v平面圖 ……………………………170 圖3.4c c>c(e)有根形式之v平面圖 ……………………………171 圖3.4d c>c(e)有根形式之v平面圖 ……………………………171 圖3.5 S2之積分路徑圖 …………………………………………172 圖3.6 S3之積分路徑圖 …………………………………………173 圖3.7a τyz(e)逆轉換路徑圖 …………………………………174 圖3.7b τyz(e)逆轉換路徑圖 …………………………………174 圖3.8a S4之積分路徑圖 …………………………………………175 圖3.9a S5之積分路徑圖 …………………………………………176 圖3.10a PZT4-Steel彈壓電複合材料之剪應力暫態圖 …………177 圖3.10b PZT4-Steel彈壓電複合材料之剪應力暫態圖 …………177 圖3.11a PZT4-Steel彈壓電複合材料之剪應力暫態圖 …………178 圖3.11b PZT4-Steel彈壓電複合材料之剪應力暫態圖 …………178 圖3.12a c>c(e)之彈壓複合材料裂紋面施加均佈載荷波前圖 …179 圖3.12b c<c(e)之彈壓複合材料裂紋面施加均佈載荷波前圖 …179 圖3.13 30°之不同彈性材料剪應力暫態圖 ……………………180 圖3.14 60°之不同彈性材料剪應力暫態圖 ……………………181 圖3.15 90°之不同彈性材料剪應力暫態圖 ……………………182 圖3.16 120°之不同彈性材料剪應力暫態圖 ……………………183 圖3.17 150°之不同彈性材料剪應力暫態圖 ……………………184 圖3.18 -30°之不同彈性材料剪應力暫態圖 ……………………185 圖3.19 -60°之不同彈性材料剪應力暫態圖 ……………………186 圖3.20 -90°之不同彈性材料剪應力暫態圖 ……………………187 圖3.21 -120°之不同彈性材料剪應力暫態圖 …………………188 圖3.22 -150°之不同彈性材料剪應力暫態圖 …………………189 圖3.23 PZT4-Steel彈壓電複合材料之電位移暫態圖 …………190 圖3.24 30°之不同彈性材料電位移暫態圖 ……………………191 圖3.25 60°之不同彈性材料電位移暫態圖 ……………………192 圖3.26 90°之不同彈性材料電位移暫態圖 ……………………193 圖3.27 120°之不同彈性材料電位移暫態圖 ……………………194 圖3.28 150°之不同彈性材料電位移暫態圖 ……………………195 圖4.1 電極型邊界描述 …………………………………………196 圖4.2 界面裂紋之問題描述 ……………………………………197 圖4.3 Γη之積分路徑圖 ………………………………………198 圖4.4 存在MT表面波之c>c(e)積分路徑圖 ……………………199 圖4.5 函數f之積分路徑圖 ……………………………………200 圖4.6 存在MT表面波之c<c(e)積分路徑圖 ……………………201 圖4.7 無MT表面波之c>c(e)積分路徑圖 ………………………202 圖4.8 無MT表面波之c<c(e)積分路徑圖 ………………………203 圖4.9 受應力負載含界面裂紋之應力強度因子 ………………204 圖4.10 受應力負載含界面裂紋之電位移強度因子 ……………205 圖4.11 數值積分示意圖 …………………………………………206 |
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